Self concordance and damped Newton method

In 1994 Nesterov and Nemirovskii introduced a unified theory of interior point methods in Convex Programming based on self-concordant functions. This concept shows the good behaviour of certain functions related to the local metric defined by themselves. Due to the Lipschitz properties of these functions, Nesterov and Nemirovski proposed a damped version of the Newton method and proved its convergence. In this paper we describe the damped Newton method and present the most relevant properties of self-concordance to prove its convergence. Finally some computational experiments are referred.